A note on Lamarle formula in Minkowski $3$-space

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Published: Dec 25, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2653
Keywords:
Pseudo-Null Curve Ruled surface Minkowski 3-space

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Ufuk Öztürk
Çankırı Karatekin University
Kazım İlarslan
Kırıkkale University
Esra Betül Koç Öztürk
Emilija Nesovic
University of Kragujevac

Abstract

The Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field in Minkowski $3$-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples.

Article Details

How to Cite
Öztürk, U., İlarslan, K., Koç Öztürk, E. B., & Nesovic, E. (2018). A note on Lamarle formula in Minkowski $3$-space. Tamkang Journal of Mathematics, 49(4), 291–300. https://doi.org/10.5556/j.tkjm.49.2018.2653
Issue
Vol. 49 No. 4 (2018)
Section
Papers
Author Biographies

Ufuk Öztürk, Çankırı Karatekin University

Department of Mathematics, Faculty of Science, University of Çankırı Karatekin, 18100 Çankırı, Turkey.

Kazım İlarslan, Kırıkkale University

Department of Mathematics, Faculty of Sciences and Art, University of Kırıkkale, 71450 Kırıkkale, Turkey.

Esra Betül Koç Öztürk

A.H.R.Mah. Çayyolu Cad. Ada Sitesi B blok No:18/12, 18100 Çankırı, Turkey.

Emilija Nesovic, University of Kragujevac

Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia.

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